STA Quiz Questions Exam 1

You are about to take the road test for your​ driver's license. You hear that only 31​% of candidates pass the test the first​ time, but the percentage rises to 79​% on subsequent retests. Estimate the average number of tests drivers take in order to get a license. Your simulation should use at least 20 runs.

1.9

Descriptive statistics refers to methods of making decisions or predictions about a​ population, based on data obtained from a sample of that​ population; while inferential statistics refers to methods for summarizing the data.

False

You randomly sample 77 people in your​ school, and none of them is a vegetarian. Does this mean that the probability of being a vegetarian for students at your school equals​ 0? Explain.

No. In the short​ run, the proportion of a given outcome can fluctuate a lot. As more people are​ sampled, the proportion should approach the real probability.

A study shows that the amount of chocolate consumed in Canada and the number of automobile accidents is positively related. Which of the following identifies a potential lurking​ variable?

Population growth

A researcher records for each participant in a clinical trial the amount of alcohol they consume per month and their cholesterol level. Indicate whether each variable is categorical or quantitative.

The alcohol variable is quantitative. The cholesterol level variable is quantitative.

Suppose you were to collect data for the pair of given variables in order to make a scatterplot. For the variables time spent on homework and exam​ grade, which is more naturally the response variable and which is the explanatory​ variable?

The explanatory variable is time spent on homework. The response variable is exam grade.

std. dev

The standard deviation represents a typical distance of an observation from the mean.

A random sample of records of electricity usage of homes in the month of July gives the amount of electricity used and size​ (in square​ feet) of 135 homes. A simple linear regression was performed to predict the amount of electricity used​ (in kilowatt-hours) based on size. The resulting model is ModifyingAbove usage with caret equals 1229 plus 0.02 size.usage=1229+0.02size. The residual for a family living in a house that is 2290 square feet is negative. Interpret.

They are using less electricity than predicted by the regression equation.

Is there intelligent life on other planets in the​ universe? If you are asked to state the probability that there​ is, would you need to rely on the relative frequency or the subjective definition of​ probability? Explain.

You would need to rely on the subjective definition because you would be relying on your own judgment.

Heights of men on a baseball team have a​ bell-shaped distribution with a mean of 168 cm and a standard deviation of 8 cm. Using the empirical​ rule, what is the approximate percentage of the men between the following​ values? a. 160 cm and 176 cm b. 152 cm and 184 cm

a. 68 b. 95

a. Explain the difference between categorical and quantitative variables. b. Give an example of a categorcal variable. c. Give an example of a quantitative variable.

a. A variable is called categorical if each observation belongs to one of a set of categories. A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable. b. gender, religion c. amount of rain, number of siblings

The job placement center at your school surveys all graduating seniors at the school. Their report about the survey provides numerical summaries such as the average starting salary and the percentage of students earning more than ​$35,000 a year. a. Are these​ descriptive, or​ inferential, statistical​ analyses? Explain. b. Are these numerical summaries better characterized as statistics or as​ parameters?

a. Descriptive, because they summarize the data collected. b. Parameters​, because the analyses summarize data on a population.

A historian wants to estimate the average age at marriage of menmen in a region in the early 19th century. Within herher ​state's archives, she finds marriage records for the years​ 1800-1820, which she treats as a sample of all marriage records from the early 19th century. The average age of the men in the records is 29.4 years. Using the appropriate statistical​ method, she estimates that the average age of grooms in the region in the early 19th century was between 28.7 and 30.1 years. a. Which part of this example gives a descriptive summary of the​ data? b. Which part of this example draws an inference about a​ population? c. To what population does the inference in part b​ refer? d. The average age of the sample was 29.4 years. Is 29.4 a statistic or a​ parameter?

a. The average age 29.4 years b. The interval of ages between 28.7 and 30.1 years c. the men in the region in the early 19th century d. statistic

dentify each of the following variables as continuous or discrete. a. The length of time to run a marathonThe length of time to run a marathon b. The number of socks in a drawerThe number of socks in a drawer c. The number of people in line at a box office to purchase theater ticketsThe number of people in line at a box office to purchase theater tickets d. The time spent in line for a rollercoaster

a. The length of time to run a marathon is a continuous variable since it has an infinite continuuman infinite continuum of possible values. b. The number of socks in a drawer is a discrete variable since it has a finite numbera finite number of possible values. c. The number of people in line at a box office to purchase theater ticketsThe number of people in line at a box office to purchase theater tickets is a discretediscrete variable since it has a finite numbera finite number of possible values. d. The time spent in line for a rollercoasterThe time spent in line for a rollercoaster is a continuouscontinuous variable since it has an infinite continuuman infinite continuum of possible values.

A couple plans to have three children. Each child is equally likely to be a girl or​ boy, with gender independent of that of the other children. a. Construct a sample space for the genders of the​ children, using B for boy and G for girl. b. Find the probability that all 3 of the children are boys. c. Answer part b​ if, in​ reality, for a given​ child, the chance of a boy is 0.480.48.

a. {BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG} b. 0.125 c. .111 (.48 cubed)

A study attempted to estimate the proportion of Florida residents who were willing to spend more tax dollars on protecting the Florida beaches from environmental disasters. ​Twenty-four hundred Florida residents were surveyed. Which of the following is the population of interest in the​ study?

all Florida residents

Planning the methods for data collection to study the effects of Vitamin E on athletic strength would be classified as which aspect of​ statistics: design,​ inference, or​ description?

design

For two events A and​ B, ​P(A)equals=​0.4, ​P(B)equals=​0.3, and​ P(A and ​B)equals=0. It follows that A and B are

disjoint but not independent

To estimate the percentage of defective items a machine is​ producing, a quality control analyst inspects the first 100 items produced in a day. This technique produces a random sample.

false

venn diagram of not disjoint events

middle shaded section

What is the probability that a randomly selected degree is not in​ Mathematics?

take the proportion of math students. subtract this number from 1

A manufacturer of cellular phones has decided that an assembly line is operating satisfactorily if less than​ 6% of the phones manufactured per day are defective. To check the quality of a​ day's production, the company decides to randomly sample 30 phones from a​ day's production and test for defects. Define the sample of interest to the manufacturer.

the 30 cellular phones that were sampled and tested